Roundness (circularity) of a surface is the requirement that every point on the surface be located between two perfect concentric circles, with the radial difference between the circles being the magnitude.
There are many methods for measuring roundness. Some methods are:                Placing the round part in a V-block and rotating it by hand with an indicator at TDC (top-dead-centre)        Measuring the diameter at several locations with a micrometer or caliper        Using a coordinate measuring machine        Taking a photo and analyzing the data with image processing software        Measuring the radius at several locations with a radius meter        Using a precision spindle assembly (such as an air bearing spindle assembly) to rotate a part with respect to an indicator, or to rotate the indicator with respect to the part        
Each of these methods has advantages and disadvantages. For example, using a precision spindle assembly to measure roundness is a simple concept but there are a few difficulties with implementing the concept. First, the centre of the part must be made coincident with the centre of the axis of rotation of a spindle assembly. This can be done mechanically by moving one or the other until they are coincident, or by recording the measured data and post-processing to remove the fundamental (1 cycle per rotation) component. This post-processing is valid because the fundamental component is effectively the eccentricity and not related to the roundness of the part. Even with post-processing, it is usually still required to centre the part to some degree.
Second, the motion of the spindle assembly itself has errors that might be significant. In general, these errors can be measured and either accepted as measurement errors, or if repeatable then accounted for.
Third, the angle of the part to be measured is relevant. It is sometimes necessary to adjust the orientation of the spindle assembly and the orientation of the axis of the measured surface to be parallel within some value. Depending on the parallelism requirement, a mechanism may be required for making this adjustment. If there is significant tilt between the axes, the result is an elliptical measured shape, which is impossible to distinguish from an actual roundness error without further testing.
Fourth, there are many other sources of measurement error including: deflection of parts due to external loading, deflection of a spindle bearing due to external loading, thermal expansion of parts in the metrology loop, indicator errors, deformation of the part due to clamping or gravity forces, and deflection of the part due to indicator contact forces.
There are two general types of precision spindle roundness testers, those where the indicator rotates and the part is fixed, and those where the part rotates and the indicator is fixed. The vast majority are of the second type.
Several other geometric characteristics are often measured with precision spindle roundness testers including: concentricity, flatness, cylindricity, runout, and surface roughness. All of these including roundness can be critical to the performance and safety of various machine elements.